A lightweight convolutional neural network to reconstruct deformation in BOS recordings

We introduce a Convolutional Neural Network (CNN) that is specifically designed and trained to post-process recordings obtained by Background Oriented Schlieren (BOS), a popular technique to visualize compressible and convective flows. To reconstruct BOS image deformation, we devised a lightweight network (LIMA) that has comparatively fewer parameters to train than the CNNs that have been previously proposed for optical flow. To train LIMA, we introduce a novel strategy based on the generation of synthetic images from random-irrotational deformation fields, which are intended to mimic those provided by real BOS recordings. This allows us to generate a large number of training examples at minimal computational cost. To assess the accuracy of the reconstructed displacements, we consider test cases consisting of synthetic images with sinusoidal displacement as well as images obtained in the experimental studies of a hot plume in air and a flow past and inside a heated hollow hemisphere. By comparing the reconstructed deformation fields using the LIMA or conventional post-processing techniques used in Direct Image Correlation (DIC) or conventional image cross-correlation, we show that LIMA is more accurate and robust in the synthetic test case. When applied to experimental BOS recordings, all methods provide similar and consistent deformation fields. As LIMA is capable of achieving a comparable or better accuracy at a fraction of the computational costs, it represents a valuable alternative to conventional post-processing techniques for BOS experiments.